Potential Energy Curves and Dissociation Energy of Ti0 ing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. c. 20036. Remit check Or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-73-2880. References and Notes
2885 (3) W. J. Mortier and H. J. Bosmans, J. PhYs. Chem., 75,3327 (1971). (4) W.J. Mortier, H. J. Bosmans, and J. B. Uytterhoeven, J. Phys. Chem.. 76. 650 i1972). (5) A . Ganguiee, J. kppl. Cryst, 3, 272 (1970). (6) W. J. Mortier and M. L. Costenoble, J. A w l . Cryst., in press. (7) W. C. Hamilton, POWOW, Brookhaven National Laboratory, Brookhaven, N. Y . , 1962. (8) W. J. Mortier, Acta Cryst., A29, 473 (1973). (9) W.R. Busing, K. 0. Martin, and H. A . Levy, ORFFE, Oak Ridge National Laboratory, Oak Ridge, Tenn., 1964. (101 > - , - J. V. Smith, Advan. Chem. Ser., No. 101,171 (1971). (11) R. J. Mikovsky, A. J. Sylvestri, E. Dempsey, and D. H . Oison, J . Catai., 22, 371 (1971). (12) W. H. Baur, Amer. Mineral., 49, 697 (1964). (13) E. Vansant, Ph.D. Thesis, Kathoiieke Universiteit te Leuven, 1971 ~
(1) B. K. G. Theng, E. Vansant, and J. B. Uytterhoeven, Trans. Faraday SOC., 64, 3370 (1968). (2) E. Vansant and J. B. Uytterhoeven, Trans. Faraday Soc., 67, 2961 (1971).
Potential Energy Curves and Dissociation Energy of Titanium Monoxide V. S. Kushawaha Department of Physics, Banaras Hindu University, Varanasi-221005, lndia (Received May 24, 1973)
Potential energy curves for Ti-0 interactions corresponding to the X3&, A”, and C3A states of the T i 0 molecule have been calculated using the method of Rydberg-Klein-Rees as modified by Vanderslice, et al. The ground-state dissociation energy has been estimated using Lippincott’s three-parameter form of the potential function and also using the chemical energy available in a chemiluminescent reaction of Tic14 + 0 2 in the presence of potassium vapor. From the chemiluminescent reaction its value was found to be 167.82 f 2 kcal/mol.
Introduction As T i 0 is observed very strongly in the spectra of M and S type stars, its spectroscopic study has been the subject of interest of many ~ o r k e r s , l -and ~ ~ seven electronic band systems are known in the region 3000-1000 A. High-resolution studies of the T i 0 bands have confirmed two singlet and three triplet states in the energy region 10000-2000 cm-l. The ground state of T i 0 is well confirmedg to be the 3Arr with a very low lying state at about 581 cm-I and a slightly higher state a t about 2295 cm-l. Uhler’sg study of the electronic spectrum of T i 0 has revised the previous designation of the molecular , and C 3 7 r to X3Ar, A34 and C3A, states from X 3 ~ rB3Z and has given a new set of molecular constants for these states only. The molecular constants of the two singlet states are st ill uncertain. The present communication deals with th,e experimental potential energy curves of these electronic states using the molecular constants reported by Uhler.9 The ground-state dissociation energy of T i 0 has been determined by a number of workers using different methods, but the values are different from each other. Do(Ti0) is 156.9 f 2.2 kcal/mol by Hampson, e t a1.,I5 167.38 f 2.30 kcal/mol by Wahlbeck, e t a1.,16 159.9 kcal/mol by Groves, e t al.,I7 157 kcal/mol by Berkowitz, e t al.,ls 158.62 kcal/rnol by Wheatley,lg 157 kcal/mol by In the Herzberg,20 and 129 kcal/mol by Carlson, e t present communication an attempt has been made to clarify the exact value of Do(Ti0) using the potential
energy curve of the ground state of T i 0 and the chemical energy available in a chemiluminescent reaction. Experimental Section Construction of t h e Potential Energy Curves. The potential energy curves have been calculated from the experimental energy levels, using the method of RydbergK l e i n - R e e ~ , ~ las - ~ modified ~ by V a n d e r ~ l i c e ,known ~~ as the RKRV method. This is a WKB method where one starts with the observed energy level E and from this calculates the maximum and minimum points of vibration. This method gives the potential function very accurately but it is restricted to known energy levels. Ginter and Battino25 have suggested an extrapolation of the RKRV curves which are best for the region of the potential curve immediately beyond the last point determined from the experimental data, but they often can be extended meaningfully to as many as twice the number of vibrational levels known experimentally or to the dissociation limit, whichever is reached first energetically. The spectroscopic data used in the calculation are given in Table I and the results of the calculation are given in Table 11. Determination o f t h e Ground-State Dissociation Energy. ( I ) Curue-Fitting Method. The method of curve fitting has been used to estimate the ground-state dissociation energy of a number of molecules. This method involves the comparison of the RKRV curves for the ground state of the molecule to an empirical potential function with different values of dissociation energies. The value of the The Journal ot Physical Chemistry, Vol. 77, No. 24, 1973
V. S. Kushawaha
2886 TABLE I: Molecular Constants (cm-I) Used in the Calculation
TABLE II: RKRV Potential Curves for the Ground and Excited States of T i 0
~~
State -
Te
C3A
A34
19434.6 14242.6
X3Ar
0
WeXe
We
837.9 866.3 1008.4
4.55 3.83 4.61
re, A
Be
Lye
0.0029 0.0032 0,0030
UVi
0.4889 1.695 0.5074 1.664 0.5355 1.620
State
v
X3AT
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
dissociation energy giving the best fit is taken to be an estimate of the actual dissociation energy. The Lippincott potential function in the modified form
has been shown to fit the RKRV potential energy curves of a large number of molecules to a very great extent. According to Steele and Lippincott,26 the factors inside the squared brackets are independent of De if we put
5> F;n
:e -
(2)i;
QeWe
b = 1.065; F = 6Be2 Now in the above expression De is varied till a good fit to the RKRV curve is obtained. This value of De is a good estimate to the dissociation energy. The result of such calculation for T i 0 is given in Table 111. (ii) Chemical Excitation of TiO. Pathak and Palmer1* have reported the electronic excitation of T i 0 in a low pressure diffusion flame of a mixture of TiCi4 + 0 2 burning in the presence of potassium vapor. The authorsI4 have reported a band system in T i 0 in the region 29003200 r\ which involves the ground state of T i 0 and a new upper electronic state D. On the basis of some previous observations on BO2? and Ge0,30 they have proposed the following reaction primarily responsible for exciting T i 0 to the new energy state D.
a
=
F/1+
-
4
TiCl(G.S)
=
+ KqG.S)
----t
TiO*
+ KCl(G.S.)
(I)
where (G.S) and the superscript asterisk refer to the ground state and the electronically excited molecule, respectively. The above reaction assumes a two-body collision process between TiCl and KO in their ground states which is a valid assumption in view of the fact that no emission was recorded by Pathak and Palmer14 from TiCl, KO, or KC1. Furthermore, at the temperature (-400°K) of the reaction, one estimates that nearly 70% of the reacting molecules would be in their ground state. Thus eq I would be quite likely. It is to be noted that Pathak and Palmer14 have observed an abrupt cutoff in the emission of Tic14 0 2 K at 2920 A. This cutoff of the emission clearly gives the upper limit of the chemical energy available in the reaction and correspond to the exothermicity of the reaction. From this observation the ground state dissociation energy of T i 0 can be caiculated. Writing the reaction I in equilibrium condition we have
+
-+
D,(TiO) 4- D,(KCl) - D,(TiC1) - &(KO) = AH, (11) where Do and AH0 represent the ground-state dissociation energy and the exothermicity of the reaction at O”K, respectively. Substituting Do(TiC1) = 101 i 20 kcal/mo1,28 &(KO) = 70 k c a l / m ~ l Do(KC1) ,~~ = 101 k c a l / m ~ l and ,~~ AH0 = 34239 cm-l = 97.82 kcal/mol in eq 11, we have Do(Ti0) = 167.82 f 20 kcal/mol. The Journal of Physical Chemistry, Voi. 77, No. 24, 1973
A34
C3Ar
O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21
cm-
503.05 1,502.23 2,492.19 3,472.93 4,444.48 5,406.75 6,359.83 7,303.69 8,238.33 9,163.75 10,079.95 10.986.93 11,884.69 12,773.23 13,652.55 14,522.65 15,383.53 16,235.32 17,077.63 17,910.85 18,734.85 19,549.63 41 7.82 1,290.83 2,141.81 2,985.13 3,820.79 4,648.79 5,469.13 6,281.81 7,086.83 7,884.19 8,673.89 9,455.93 10,230.31 10,997.03 11,756.09 12,507.49 13,251.23 13,987.31 14,715.73 15,436.49 419.08 1,246.61 2,066.31 2,876.91 3,678.41 4,470.81 5,254.11 6,028.31 6,793.41 7,549.41 8,296.31 9,034.11 9,762.81 10,482.41 11,192.91 11,894.31 12,686.61 13,269.81 13,943.91 14,608.91 15,264.81 15,911.61
rwn, A
1.5936 1.5592 1.5358 1.5195 1.5068 1.4965 1.4878 1.4804 1.4740 1.4684 1.4636 1.4593 1.4556 1.4524 1.4495 1.4471 1.4450 1.4432 1.4418 1.4406 1.4397 1.4390 1.6392 1.5997 1.5751 1.5581 1.5451 1.5347 1.5260 1.5187 1.5126 1.5074 1.5029 1.4991 1.4960 1.4933 1.4912 1.4894 1.4881 1.4872 1.4866 1.4864 1.6666 1.6288 1.6033 1.5854 1.5715 1.5602 1.5506 1.5425 1.5355 1.5293 1.5240 1.5192 1.5151 1.5114 1.5083 1.5055 1.5031 1.501 1 1.4994 1.4980 1.5968 1.4960
rmfix,
A
1.6558 1.7095 1.7491 1.7818 1.8109 1.8378 1.8632 1.8875 1.9110 1.9339 1.9563 1.9782 1.9999 2.0212 2.0424 2.0635 2.0844 2.1052 2.1260 2.1467 2.1674 2.1882 1.7011 1.7618 1.8052 1.8410 1.8730 1.9027 1.9307 1.9576 1.9836 2.0089 2.0337 2.0581 2.0821 2.1059 2.1295 2.1530 2.1763 2.1995 2.2228 2.2460 1.7493 1.7539 I .8378 1.8739 1.9062 1.9362 1.9646 1.9918 2.0181 2.0438 2.0690 2.0937 2.1182 2.1425 2.1665 2.1905 2.2143 2.2382 2.2620 2.2858 2.3097 2.3337
Te
+ U,
cm-’
503.05 1,502.23 2,492.19 3,472.93 4,444.48 5,406.75 6,359.83 7,303.69 8,238.33 9,163.75 10.079.95 10.986.93 11,884.69 12,773.23 13,652.55 14,522.65 15,38353 16,235.19 17,077.63 17,910.85 18,734.85 1 9,549.63 14,660.42 1 5,533.43 16.384.41 17,227.73 18.083.39 18,891.39 19,711.73 20,524.41 21,329.43 22,126.79 22,916.49 23,698.53 24,472.91 25,239.63 25,998.69 26,750.09 27,493.83 28,229.91 28,958.33 29,679.09 19,853.68 20,681.21 21,500.91 22,311.51 23,113.01 23,905.41 24,688.71 25,462.91 26,228.01 26,984.01 27,730.91 28,468.71 29,197.41 29,917.01 30,627.51 31,328.91 32,021.21 32,704.41 33,378.51 34,043.51 34,699.41 35,346.21
Potential Energy Curves and Dissociation Energy of T i 0 TABLE I II: Calculations for the Ground-State Dissociation Energy of the T i 0 Molecule Using the Lippincott Function (Three-Parameter Form)
r,
A
1.6558 1.7095 1.7818 1.81 09 1.8632 1,9110 1.9563 1.9782 2.0212 2.0635 1.5358 1.4965 1.4804 1.4684 1.4556 1.4495 1.4450 1.4432 1.4406 1.4390
De = 60,000, De = 58,500, De = 56,000, cm-' cm-I cm-'
533.13 1 ,!i59.28 3,551.91 4,573.45 6,478.61 9,382.35 10,288.71 11,352.63 13,086.92 14,'769.8 1 2,610,73 5,521.37 7,414.81 9,275.38 12,165.91 13,858.72 15,585.23 16,462.11 18,186.25 19,814.61
506.21 1,525,31 3,501.81 4 3 1 1.35 6,398.20 8,290.51 10,103.62 11,054.43 12,821.21 14,572.74 2,512.62 5,441.32 7,343.29 9,180.87 11,921.37 13,691.38 15,431.03 16,275.61 17,971.64 19,580.52
441.15 1,420.1 0 3,380.32 4,354.71 6,240.38 8,108.67 9,882.25 10,663.35 12,493.82 14,222.65 2,422.53 5,319.62 7,228.84 9,092.63 11,312.80 13,198.61 15,065.39 15,876.27 17,501.72 19,336.11
30000
I
RKRY, crn -
503.05 1,502.23 3,472.93 4,444.45 6,359.83 8,238.33 10,079.95 10,986.93 12,773.23 14,522.60 2,492.19 5,406.75 7,303.69 9,163.75 11,884.69 13,652.55 15,383.53 16,235.19 17,910.85 19,549.63
t
20000 20000-
5 fv=o j * 3 +
, l
b
+ I +
c
Results and Discussion The experimental potential energy curves for the three states of T i 0 are shown in Figure 1. The most prominent feature of these curves is that these are narrow well type potentials which indicate that the molecule behaves approximately like a harmonic oscillator rather than an anharmonic oscillator. The ground-state potential curve is comparatively narrower than the upper state potential curve and therefore, one should expect a large value of we in the ground state than in the upper states which explains the observed we value for the lower and the upper states. The three curves are lying approximately one above the other which indicates that the structure of the molecule in the ground and in the upper states should be nearly the same. The observed re values corresponding to the X 3 A r , A34, and C3& states are nearly equal and support the predicted structure of the molecule. In addition, the Franck-Condon principle is also satisfied and thus it explains the maximum intensity of the (0,O) band and slightly lesser intensity of the (0,l) and (1,O) bands observed in the A-X and C-X band systems of TiO. The most interesting feature would be due to the presence of the potential curve of the C3A state which is inside the potential curve of the A34 state. Because of the presence of this potential curve a strong perturbation should be observed in the A-X and C-X systems. This explains the perturbation observed by Phillips7 in the A-X system but such perturbation has not been observed in the C-X system. In the analogous molecule ZrO, similar perturbations have been observed in the A-X and C-X systems.g The results of calculation for the ground-state dissociation energy of T i 0 is given in Table 111. This table shows that the best fit to the RKRV curve is obtained when we put De = 58,500 cm-l. The most probable value of De from our calculations is 166.75 kcal/mol from which we get Do(Ti0) = 165.37 kcal/mol. From the consideration of the chemical energy available in the chemiluminescent reaction, we have observed a value Do(Ti0) = 167.82 20 kcal/mol. The magnitude of the two results is in very
*
Rc I N
R
Figure 1. Potential energy curves for TiO.
good agreement, but each of them is larger than the spectroscopic valuez0 of 157 kcal/mol derived from the linear Birge-Sponer extrapolation of the ground state and also larger than the theoretical valuel2 of 129 kcal/mol. However, the present values are nearly equal to the value 167.38 k 2.30 kcal/mol reported by Wahlbeck, et ~ 1 The spectroscopic value is based on only five vibrational spacings which add to about one-tenth the dissociation energy and the theoretical result is low because of the limited basis set and the uncertainty in the correlation data. The value of Do(Ti0) reported by Hampson, et a 1 . , I 5 depends directly on the dissociation energy of ScO(g), which in turn depends on mass spectroscopic measurements involving numerous other oxides and metal species, notably those of lanthanum, yttrium, germanium, and silicon. In the abscence of a spectroscopic dissociation energy for a gaseous metal monoxide, the authors15 have reported that the dissociation energy of T i 0 is less satisfactory. Moreover, they have also admitted that there could be an error in Do(Sc0) and hence in Do(TiO), due to an inaccurate relative ionization cross section of TiO(g) and TiOZ(g). The result of Walhbeck, et a2 ,I6 seems to be more accurate than any other value of Do(Ti0) reported previously, but it is to be noted that these a u t h o r P were unable to pin down the principal reaction responsible for the vaporization of Ti305(S). Of course, they performed some relatively crude mass spectroscopic measurements to identify the principal species but all these measurements were not in agreement and therefore the dissociation enerThe Journalof Physical Chemistry, Vol. 77, No. 24, 1973
.
~
~
2888
Abha
gy of TiO(g) obtained using such measurements may not be very accurate. In the present work, we have obtained a value Do(TiO) = 167.82 f 20 kcal/mol using the position of a band head which corresponds to the highest value of the chemical energy available in the reaction and the precision of measurement of this band head is f 5 cm-I.I4 The value of the ground-state dissociation energy of Ti0 reported in this work may therefore be regarded as much more reliable than any other value, We have obtained Do(Ti0) experimentally as well theoretically, which matches very well with the value of Do(TiO)16 obtained using entirely different experimental procedure. This agreement provides strong evidence in support to the high value of Do(TiC1) 101 f 20 kcal/ rather than a low value &(TiCl) == 25 kcal/mol derived from a linear Birge-Sponer extrapolation of the ground state. Also, a comparison of Do(Ti0) = 167.82 f 20 kcal/mol (present work) and Do(Ti0) = 167.38 f 2.3 keal/moll6 shows that the uncertain value (*20 kcal/moI) in the present work (this is due to Do(TiC1)) should be the same as in Wahlbeck's16 result since the magnitude of the certain value is equal, and thus the Do(TiC1) and Do(Ti0) may be equal to 101 f 2 and 167.82 2 kcal/mol, respectively.
*
Acknowledgments. The author is thankful to Dr. C. M. Pathak for valuable suggestions and criticisms and to Mr. B. P. Asthana for help in some portions of the caleulations. The financial support received from the C.S.I.R., India, is gratefully acknowledged.
Guota and C. N.
R. Rao
References and Notes (1) (2) (3) (4)
A. Fowler, Proc. Phys. SOC.,London, 19A, 509 (1907). F. Lowater, Proc. Phys. SOC., London, 41, 557 (1929). K. Wurn and M. J. Meister, 2.Astrophys., 13, 199 (1937). C. C. Kiess, Publ. Astron. SOC.Pac.. 6 0 , 252 (1937). (5) F. P. Coheur, Bull. SOC.Roy. Sci. Liege, 12,98 (1943). (6) J. G. Phillips, Astrophys. J., 111, 314 (1950). (7) J. G. Phillips, Astrophys. J., 114, 152 (1951). (8) J. G. Phillips,Astrophys. J., 115, 567 (1952). (9) U. Uhier, Ph.D. Thesis, University of Stockholm, Sweden, 1954. ( 1 0 ) A. V. Petterson, Ark. Fys., 16, 185 (1959). (11) A. V. Petterson and B. Lindgren, Naturwissenschaften, 48, 128 (1961). (12) K. D. Carlson and R. K. Nes, J. Chem. Phys., 41, 1051 (1964). (13) I. Kovacs and V. M. Korwar, Acta. Phys. Hung., 29, 399 (1970). (14) C. M. Pathak and H. B. Palmer, J. Mol. Spectrosc., 33, 137 (1970). (15) P. J. Hampson and P. W. Gilles, J. Chem. Phys., 55, 3712 (1971). (16) P. G. Wahlbeck and P. W. Gilles, J. Chern. Phys., 46, 2465 (1967). (17) W. 0. Groves, M. Hoch, and H. L. Johnston, J. Phys. Chern., 59, 127 (1955). (18) J. Berkowitz, W. A. Chupka, and M. G. Inghram, J . Phys. Chem., 61, 1569 (1957). (19) Q. D. Wheatley, Ph.D. Thesis, Universityof Kansas, 1954. (20) G. Herzberg, "Spectra of Diatomic Molecules," D. Van Nostrand, Princeton, N . J., 1950. (21) R. Rydberg, Z. Phys., 73, 376 (1931); 80, 514 (1933). (22) 0. Klein, Z. Phys., 76, 226 (1932). (23) A. L. G. Rees, Proc. Roy. SOC.,Ser. A, 59, 998 (1947). (24) J. T. Vanderslice, E. A. Mason, W. G. Maisch, and E. R. Lippincott, J. Mol. Spectrosc., 3, 17 (1959); 5, 83 (1960). (25) M. L. Ginter and R. Battino, J. Chem. Phys., 42, 3222 (1965). (26) D. Steele, E. R. Lippincott, and J. T. Vanderslice, Rev. Mod. Phys., 34,239 (1962). (27) D. W. Naegii, Ph.D. Thesis, Pennsylvania State University, 1967. (28) V. I. Vedeneyev, et a/., "Bond Energies, Ionization Potentials and Electron Affinities," U.S.S.R. Academy of Sciences, 1962. (29) A. G. Gaydon, "Dissociation Energies," 3rd ed, Chapman and Hall, London, 1968. (30) H. B. Palmer, A. Tewarson, D. W. Naegeli, and C. M. Pathak, "Molecular Luminescence," E. C. Lim, Ed., Mi. A. Benjamin, New York, N. Y., 1969. p 493.
CNDO/P Studies on Ion Solvation Abha Gupta and C. N. Fa. Rao* Department of Chemistry, lndian institute of Technology, Kanpur-16, lndia (Received April 18, 7973)
CNDO/2 calculations on the interaction of Li+ with a variety of donor molecules such as H20, ether, carbonyl compounds, XH3, acetonitrile, pyridine, and HF to give complexes of the type Li+(donor), show that the binding energy decreases whiie the Lit-donor distance increases with increase in n. These calculations satisfactorily describe the nature of charge transfer in these complexes as well as their stereochemistry. The changes in bond distances and spectral properties of carbonyl donors due to complexation are also predicted. The potential energy surfaces obtained from the study can be fitted into the Lennard-Jones 6-12 potential function. Based on the CND0/2 calculations, comments have been made regarding the nature of the second hydration layer, different types of ion pairs, and the quantized vibrations of L i t in solvent cages.
Solvation of ions in aqueous and nonaqueous media is of primary importance in the theory of poiar liquids. It appeals to reason that in the region of the primary solvation sphere where the ion is closest to solvent molecules there will be strong interaction, while a t large distances the solvent is essentially unperturbed. We can also visualize an intermediate region where the solvent molecules are The Journalof Pbysical'Cbernistry, Vol. 77, No. 24, 7973
slightly perturbed and there is some disorder in the solvent structure. Although classical models1T2 are somewhat successful in the study of ion-dipole interactions, they provide little information on the electronic structure of the solvated ions and on the nature of binding forces. However, semiernpirical LCAO M O SCF methods would be particularly useful in examining ion-solvent complexes,
